Abstract: Homogeneity of between-individual variances and/or autocorrelation coefficients is one of standard assumptions in longitudinal analysis. However, this assumption needs to be tested statistically. Zhang \& Weiss$^{[15]}$ discussed the tests for heterogeneity of between - and/or within-individual variances in linear models with random effects. Lin \& Wei$^{[10]}$ considered the tests for homogeneity of between-individual autocorrelation
coefficients in nonlinear models with AR(1) errors but without random effects. However, for such models, the tests for homogeneity of autocorrelation coefficients between individuals as autocorrelation on all individuals exists, have not been considered. This paper is devoted to the tests for homogeneity of between-individual variances and/or autocorrelation coefficients
in the framework of nonlinear regression models with random effects and AR(1) errors. Several diagnostic tests using score statistic are constructed. The properties of test statistics are nvestigated through Monte Carlo simulations. An real-data and simulated-dat examples are analyzed in Section 5 to illustrate the proposed methodology.

Key words: AR(1) errors, Autocorrelation coefficient, Heteroscedasticity, Nonlinear regression, Random effects, Score test